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Today, overlay networks are used as a promising platform to deploy wide area of applications and services in the Internet. The application level state maintained by the overlay networks should have high degree of availability.This can be compromised when a significant percentage of overlay nodes fails simultaneously (massive failure). The first problem: when a significant fraction of nodes fails simultaneously the loss rate increases awfully. The second problem: End-to-end latency increases dramatically when massive failure occurs. The third problem: in some overlay networks, an adversary can discover connectivity information of routing path easily and consequently he can prevent communication by attacking only the specific nodes.Random path diversity (RPD) is a technique that we use to handle such problems. This paper shows that how sending the same packet through few overlay paths in a random manner improves robustness of overlay networks against massive failure and routing path discovery. The chord network is a case study of this paper.Experimental results show RPD makes the chord overlay network more robust against massive failure. Results show 4-RPD (i.e. simultaneously sending the same packet through four different paths) improves resilience of Chord against massive failure on average 40%. It also reduces end-to-end latency made by massive failure more than 30% (on average). By the way randomness gives the network anonymity that makes network more complicated for routing path discovery. Results show 4-RPD improves anonymity more than 55% in compare to no diversity.